Beurling-Fourier algebras on compact groups: spectral theory

2011/03/21 by Ludwig, Jean, Spronk, Nico, Turowska, Lyudmila
#22E30 #43A45 #43A77 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 43A30 #Secondary 46M20

paper · doi:10.48550/arxiv.1103.4063

Abstract

For a compact group G we define the Beurling-Fourier algebra A_ω(G) on G for weights ω defined on the dual \what G and taking positive values. The classical Fourier algebra corresponds to the case ω is the constant weight 1. We study the Gelfand spectrum of the algebra realizing it as a subset of the complexification G_{\mathbb C} defined by McKennon and Cartwright and McMullen. In many cases, such as for polynomial weights, the spectrum is simply G. We discuss the questions when the algebra A_ω(G) is symmetric and regular. We also obtain various results concerning spectral synthesis for A_ω(G).

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